In recent years toothpaste dispensers have become widely available in which a relatively large volume of paste is contained in a free standing container, and a piston-and-cylinder dispenser pump with a fixed discharge nozzle is provided at the top of the container to dispense a dose of toothpaste when the pump piston is depressed. Known pumps include arrangements for covering, blocking or shielding the discharge nozzle outlet between operations of the pump to keep the residual paste in the pump from drying out and to help separate the tail end of each dispensed dose from the nozzle end. Toothpaste is extremely sticky and there are often problems in that slugs of paste issuing forth are not cleanly cut off, leading to toothpaste being smeared on the outside of the discharge nozzle by the cover arrangement which is precisely the opposite of what is wanted.